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Sets of Formulas Valid in Finite Structures

1973
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Transactions of the American Mathematical Society
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line ^4 d-{V ) « d(V ) vdfVJ, SETS OF FORMULAS VALID IN FINITE STRUCTURES Abstract A function Ir is defined on the set of all subsets of u) so that for each set K, the value, Ir , is the set of formulas K valid in all structures of cardinality in K. An analysis is made of the dependence of \s on K. It is easily seen that K for all infinite sets K, d(K) V 1 £ d(K) £ d(K) ! . On the other hand, we prove that d(U ) = d(lr ) = d(U ) , and use this tõ KVj ^ K ~ u prove that for any two degrees a and

doi:10.2307/1996611
fatcat:rac7aqrqxvgpfegy6peul43xem